Our objective is to ensure that observing or querying the value function in Algorithm REF  will not reveal useful information about rewards received by an agent.
This is formally stated in Theorem REF , which establishes a guarantee on the privacy of Algorithm REF .
We make an assumption to ensure that the neural networks used to learn \(Q^\theta _{cpt}(s,a)\)  define a complete vector space of functions equipped with a norm that is a combination of \(L^p-\) norms of the functions along with some of its derivatives.
Then, we state intermediate results which establish i) conditions for \((\epsilon , \delta )-\) differential privacy of a mechanism \(\mathbb {M}\)  [1]}, [2]}, [3]}, ii) that sample paths of a Gaussian process generated on a reproducing kernel Hilbert space (RKHS) are bounded with high probability [3]}, and iii) an expression for the RKHS norm [3]}, [6]}.
